Abstract : The integration of memristive nanodevices within transistor-based electronic systems offers the potential for computing structures smaller, lower power and cheaper than traditional high-performance systems. Among emerging memristive technologies, a novel device based on organic materials distinguishes itself, in that it can feature several threshold voltages on the same die, and possesses unipolar behavior. In this work, we highlight that these two features can be beneficial for neural network-inspired learning systems. An on-chip supervised learning method for hybrid memristors / CMOS systems — an analogue synaptic array paired with a hybrid learning cell — is extended to the case of this novel organic memristor device. The organic device can be trained with only one pulse per row (two for the entire array) per presentation of input — as compared to four for a bipolar memristor array. The device also works universally- in both the synaptic grid as well as learning cell-paving the way to single die integration. The proposed scheme learns successfully, even while incorporating non-ideal circuit phenomena such as a wide range of parasitic wire resistances and associated sneak paths. These encouraging first results suggest that these multi-threshold, unipolar organic memristive devices are a useful species for inclusion in adaptive next generation electronic systems